It is very possible that what you're experiencing is an allergic reaction. With allergic reactions, the most common skin manifestations are dryness and hives. Definitive diagnosis is done with allergy testing but you don't need to go to that extent to figure it out. Obvious first step would be to stop using PG. If the dryness resolves, then you have your answer. Oral antihistamines will help and cetirizine (Zyrtec) and diphenhydramine (Benadryl) are good over-the-counter choices; diphenhydramine is the more potent one but also has a stronger sedating effect. If you're experiencing any redness or itchiness, you could also use topical corticosteroid creams (1-2% hydrocortisone).
In relation to the comments on nicotine: it is a skin irritant, but unless you're getting it directly on your face then that's not the cause. Nicotine can cause a dryness of the skin and premature aging, but it won't show up in a patchy distribution.